﻿ Taylor Class   # Taylor Class

Taylor series expansions for common functions. Inheritance Hierarchy
SystemObject
Accord.MathTaylor

Namespace:  Accord.Math
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0 Syntax
`public static class Taylor`

The Taylor type exposes the following members. Methods
NameDescription  Cos
Returns the cosine of a specified angle by evaluating a Taylor series.  Cosh
Returns the hyperbolic cosine of a specified angle by evaluating a Taylor series.  Exp
Returns e raised to the specified power by evaluating a Taylor series.  Sin
Returns the sine of a specified angle by evaluating a Taylor series.  Sinh
Returns the hyperbolic sine of a specified angle by evaluating a Taylor series.
Top Remarks

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

The concept of a Taylor series was discovered by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor series is centered at zero, then that series is also called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.

It is common practice to approximate a function by using a finite number of terms of its Taylor series. Taylor's theorem gives quantitative estimates on the error in this approximation. Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial. The Taylor series of a function is the limit of that function's Taylor polynomials, provided that the limit exists. A function may not be equal to its Taylor series, even if its Taylor series converges at every point. A function that is equal to its Taylor series in an open interval (or a disc in the complex plane) is known as an analytic function in that interval.

References: See Also